A wire elongates by $ l \,mm$ when a load w is hanged from it. If the wire goes over a pulley and two weights w each are hung at the two ends, the elongation of the wire will be (in mm):
Let us consider the length of wire as $L$ and cross-sectional area $A$, the material of wire has Young's modulus as $Y$.
Then for $1\,st$ case, $Y=\frac{w / A}{V L}$ For $2\,nd$ case, $Y=\frac{w / A}{2 l^{'} / L}$ $\therefore l^{'}=\frac{l}{2}$ So, total elongation of both sides $=2 l^{'}=l$
Mechanical properties of solids intricate the characteristics such as the resistance to deformation and their strength. Strength is the ability of an object to resist the applied stress, to what extent can it bear the stress.
Therefore, some of the mechanical properties of solids involve:
Elasticity: When an object is stretched, it changes its shape and when we leave, it retrieves its shape. Or we can say it is the property of retrieving the original shape once the external force is removed. For example Spring
Plasticity: When an object changes its shape and never attains its original shape even when an external force is removed. It is the permanent deformation property. For example Plastic materials.
Ductility: When an object is been pulled in thin sheets, wires or plates, it will be assumed that it has ductile properties. It is the property of drawing into thin wires/sheets/plates. For example Gold or Silver
Strength: The ability to hold out applied stress without failure. Many types of objects have higher strength than others.
